Simplify to lowest terms. $\dfrac{70}{80}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 70 and 80? $70 = 2\cdot5\cdot7$ $80 = 2\cdot2\cdot2\cdot2\cdot5$ $\mbox{GCD}(70, 80) = 2\cdot5 = 10$ $\dfrac{70}{80} = \dfrac{7 \cdot 10}{ 8\cdot 10}$ $\hphantom{\dfrac{70}{80}} = \dfrac{7}{8} \cdot \dfrac{10}{10}$ $\hphantom{\dfrac{70}{80}} = \dfrac{7}{8} \cdot 1$ $\hphantom{\dfrac{70}{80}} = \dfrac{7}{8}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{70}{80}= \dfrac{2\cdot35}{2\cdot40}= \dfrac{2\cdot 5\cdot7}{2\cdot 5\cdot8}= \dfrac{7}{8}$